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\subsection{dstms--001 --- The birth-death process}

\subsubsection{dstms--001--01}

This model contains one species, denoted by $X$. The amount of $X$ present
in the system is measured in numbers of molecules. The initial number
of molecules of $X$ is 100. The birth reaction 
\[
X \longrightarrow 2X
\] has global rate
parameter \verb$Lambda=0.1$. The death reaction 
\[
X \longrightarrow \emptyset
\]
has global rate parameter \verb$Mu=0.11$. Mass-action stochastic
kinetics is assumed. The SBML-shorthand for the model is stored in the
file \verb$dsmts-001-01.mod$, and this is intended to be
human-readable and self-documenting. The SBML file itself is stored in
\verb$dsmts-001-01.xml$, and this is generated automatically from the
corresponding SBML-shorthand. The mean and standard deviation of the
associated Markov process are given in the plots below, and are stored
in the files \verb$dsmts-001-01-mean.csv$ and
\verb$dsmts-001-01-sd.csv$ respectively.

\addplots{dsmts-001-01}

\subsubsection{dsmts--001--02}

This model is the same as \texttt{dsmts-001-01}, except that the rate
parameters \verb$Lambda$ and \verb$Mu$ are declared to be local rather
than global.

\addplots{dsmts-001-02}

\subsubsection{dsmts--001--03}

This model is the same as \texttt{dsmts-001-01}, except
that the values of the rate parameters are \verb$Lambda=1$ and
\verb$Mu=1.1$. The skewed distribution associated with this model
means that simulators are likely to fail the suggested standard
deviation test for large values of \verb$t$ (as the normality
assumption underlying the test is clearly invalid in this case).

\addplots{dsmts-001-03}

\subsubsection{dsmts--001--04}

This is the same as \verb$dsmts-001-01$, except that the initial
number of molecules of \verb$X$ is 10.

\addplots{dsmts-001-04}

\subsubsection{dsmts--001--05}

The same as \verb$dsmts-001-01$, except that the initial number of molecules
of X is 10,000. Due to the large number of molecules involved, tests
using this model will take longer to complete than for many other
models in the suite.

\addplots{dsmts-001-05}

\subsubsection{dsmts--001--06}

The same as \verb$dsmts-001-01$, except that: (i) There is
another species, named \texttt{Sink}, with initial amount 0. The
\verb$Sink$ species 
is declared to be a boundary condition. (ii) The death reaction is
now:
\[
X \longrightarrow Sink 
\]
This model checks that the boundary condition attribute is handled
correctly.

\addplots{dsmts-001-06}

\subsubsection{dsmts--001--07}

The same as \verb$dsmts-001-06$, except that the \texttt{Sink} species is not
a boundary condition. This model is the first one involving two time-varying
species.

\addplots{dsmts-001-07}

\subsubsection{dsmts--001--08}

Same as \verb$dsmts-001-01$, except that the \verb$Cell$
compartment is declared to have \verb$size=1$. This shouldn't affect
anything.

\addplots{dsmts-001-08}

\subsubsection{dsmts--001--09}

 Same as \verb$dsmts-001-01$, except
that the \verb$Cell$ compartment is declared to have
\verb$size=2$. Again, this shouldn't affect anything, due to the
presence of the \verb$hasOnlySubstanceUnits$ flag in the species
declaration.

\addplots{dsmts-001-09}

\subsubsection{dsmts--001--10}

Same as
\verb$dsmts-001-01$, except that: (i) the \verb$Cell$ compartment is
declared to have 
\verb$size=1$ (ii) \verb$hasOnlySubstanceUnits$ is not declared to be
true. Although many simulators will mis-interpret this model, most
will get the right output due to the unit compartmental size. 

\addplots{dsmts-001-10}

\subsubsection{dsmts--001--11}

This is the same as \verb$dsmts-001-01$, except that: (i) the
\verb$Cell$ compartment is declared to 
have \verb$size=2$ (ii) \verb$hasOnlySubstanceUnits$ is not declared
to be true. Many simulators (which pass the earlier tests) are
expected to fail this test, due to a lack of sophisticated handling of
the \verb$hasOnlySubstanceUnits$ tag. It would be reasonable for a
simulator to refuse to accept such a model, but a simulator should not
accept the model and then produce incorrect output.

\addplots{dsmts-001-11}

\subsubsection{dsmts--001--12}

This is the same as \verb$dsmts-001-01$, except that the rate law is
written as \verb$Lambda*X*0.5*2$. This is designed to test the math
expression parsing.

\addplots{dsmts-001-12}

\subsubsection{dsmts--001--13}

This is the same as \verb$dsmts-001-01$, except that \verb$Lambda=0.2$
and the rate law is
written as \verb$Lambda*X*0.5$. This is designed to test the math
expression parsing.

\addplots{dsmts-001-13}

\subsubsection{dsmts--001--14}

This is the same as \verb$dsmts-001-01$, except that the rate law is
written as \verb$Lambda*X/2/0.5$. This is designed to test the math
expression parsing.

\addplots{dsmts-001-14}

\subsubsection{dsmts--001--15}

This is the same as \verb$dsmts-001-01$, except that the rate law is
written as \verb$Lambda*(X/2)/0.5$. This is designed to test the math
expression parsing.

\addplots{dsmts-001-15}

\subsubsection{dsmts--001--16}

This is the same as \verb$dsmts-001-01$, except that the rate law is
written as \verb$Lambda*X/(2/2)$. This is designed to test the math
expression parsing.

\addplots{dsmts-001-16}

\subsection{dsmts--002 --- The
immigration-death process}

\subsubsection{dsmts--002--01}

This model contains one species,
denoted by $X$. The amount of $X$ present in the system is measured in
numbers of molecules. The initial number of molecules of $X$ is $0$. The
immigration reaction 
\[
\emptyset \longrightarrow X
\]
 has global rate parameter \texttt{Alpha=1}. The death
reaction $X\longrightarrow \emptyset$ has global rate parameter
\texttt{Mu=0.1}. Mass-action stochastic kinetics is assumed.

\addplots{dsmts-002-01}

\subsubsection{dsmts--002--02}

 Same as \verb$dsmts-002-01$,
except that \verb$Alpha=10$. 

\addplots{dsmts-002-02}

\subsubsection{dsmts--002--03}

 Same as \verb$dsmts-002-02$, except the global
parameter \verb$Alpha=10$ is overridden by the local parameter
\verb$Alpha=5$. This is the first model that checks that local
parameters overload global parameters.

\addplots{dsmts-002-03}

\subsubsection{dsmts--002--04}

Same as \verb$dsmts-002-01$, except that \verb$Alpha=1000$. This model
will be slow to run.

\addplots{dsmts-002-04}

\subsubsection{dsmts--002--05}

 Same as
\verb$dsmts-002-02$, except that: (i) There are two additional species: \verb$Source$ and
\verb$Sink$. \verb$Source$ and \verb$Sink$ are both boundary conditions, and they both have
initial amount 0. (ii) The immigration reaction is now: 
\[
Source \longrightarrow X. 
\]
(iii)
The death reaction is now:
\[
X \longrightarrow Sink 
\]

\addplots{dsmts-002-05}

\subsubsection{dsmts--002--06}

 Same as \verb$dsmts-002-05$, except that
the \verb$Sink$ species is not a boundary condition. 

\addplots{dsmts-002-06}

\subsubsection{dsmts--002--07}

 Same as \verb$dsmts-002-05$,
except that the Sink species is a constant boundary condition. 

\addplots{dsmts-002-07}

\subsubsection{dsmts--002--08}

Same as \verb$dsmts-002-01$, except that: (i) The global rate parameter \verb$k$ is set
equal to 2. (ii) In the immigration rate, \verb$k$ is locally set equal to 1
(iii) In the death rate, \verb$k$ is locally set equal to 0.1. This model is
designed to test parameter overloading. 

\addplots{dsmts-002-08}

\subsection{dsmts--003 ---
Dimerisation }

\subsubsection{dsmts--003--01}

 This model contains two species, denoted by \verb$P$ and
\verb$P2$, representing a dimerisation process. The initial numbers of
molecules of P and P2 are 100 and 0 respectively. The dimerization
reaction
\[
2P \longrightarrow P2
\]
 has global rate
parameter \verb$k1=0.001$. Note that this is a second order reaction with
rate law \verb$k1*P*(P-1)/2$. The dissociation reaction 
\[
P2 \longrightarrow 2P
\] has global rate
parameter \verb$k2=0.01$. 

\addplots{dsmts-003-01}

\subsubsection{dsmts--003--02}

 Same as \verb$dsmts-003-01$, except that: (i) the initial
number of molecules of \verb$P$ is 1000 (ii) the values of the rate
parameters are \verb$k1=0.0002$ and \verb$k2=0.004$. 

\addplots{dsmts-003-02}

\subsubsection{dsmts--003--03}

 Same as \verb$dsmts-003-01$, except
that in the event that the time parameter \verb$t$ becomes greater than or
equal to 25, the species populations are reset to the following
values: \verb$P := 100$, \verb$P2 := 0$. This is the first model that
tests the SBML \verb$event$ facility.

\addplots{dsmts-003-03}

\subsubsection{dsmts--003--04}

 Same as \verb$dsmts-003-01$, except that in the event
that the number of \verb$P2$ molecules becomes greater than 30, the species
populations are reset to the following values: \verb$P := 100$,
\verb$P2 := 0$. This is another test of SBML event handling.

\addplots{dsmts-003-04}

\subsubsection{dsmts--003--05}

 Same as \verb$dsmts-003-01$, except that \verb$P$ has been removed
from the model using the conservation law present in the system. This
tests several things, including complex math expression parsing.

\addplots{dsmts-003-05}

\subsubsection{dsmts--003--06}

 Same as \verb$dsmts-003-05$, except that the rate law is written
slightly differently. This is testing the expression parser.

\addplots{dsmts-003-06}

\subsubsection{dsmts--003--07}

 Same as \verb$dsmts-003-06$, except that the rate law is written
very slightly differently. This is testing the expression parser.

\addplots{dsmts-003-07}








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